Question

If we study the vibration of a pipe open at both ends, then the following statement is not true

• A. Open end will be anti-node
• B. Odd harmonics of the fundamental frequency will be generated
• C. All harmonics of the fundamental frequency will be generated
• D. Pressure change will be maximum at both ends

Answer 1

The Correct Option is D

When studying the vibrations of a pipe open at both ends, it is important to understand the nature of standing waves formed in such a system. Let's examine each statement:

1. Open end will be anti-node:
   • In a pipe open at both ends, the open ends always act as anti-nodes for the displacement of the air particles. Hence, this statement is true.
2. Odd harmonics of the fundamental frequency will be generated:
   • This statement is inaccurate for pipes open at both ends. In fact, both odd and even harmonics of the fundamental frequency are generated, not just the odd harmonics. Therefore, odd harmonics are also present, but not exclusively.
3. All harmonics of the fundamental frequency will be generated:
   • In pipes open at both ends, all harmonics (both odd and even) of the fundamental frequency can indeed be present. Therefore, this statement is true.
4. Pressure change will be maximum at both ends:
   • The pressure changes are minimal at the open ends because these points are displacement anti-nodes and pressure nodes. In open pipes, maximum pressure change happens at nodes inside the pipe, not at the ends.
   • Thus, this statement is not true, which makes it the correct choice for this question.

Conclusively, for an open pipe at both ends, the statement "Pressure change will be maximum at both ends" is incorrect. The correct answer is: Pressure change will be maximum at both ends.